The positioning of a moving platform, such as, wheel-based platforms/vehicles or individuals, is commonly achieved using known reference-based systems, such as the Global Navigation Satellite Systems (GNSS). The GNSS comprises a group of satellites that transmit encoded signals to receivers on the ground that, by means of trilateration techniques, can calculate their position using the travel time of the satellites' signals and information about the satellites' current location. Such positioning techniques are also commonly utilized to position a device (such as for example, among others, a mobile phone) within or on the moving platform, whether such device is tethered or non-tethered to the moving platform.
Currently, the most popular form of GNSS for obtaining absolute position measurements is the global positioning system (GPS), which is capable of providing accurate position and velocity information provided that there is sufficient satellite coverage. However, where the satellite signal becomes disrupted or blocked such as, for example, in urban settings, tunnels and other GNSS-degraded or GNSS-denied environments, a degradation or interruption or “gap” in the GPS positioning information can result.
In order to achieve more accurate, consistent and uninterrupted positioning information, GNSS information may be augmented with additional positioning information obtained from complementary positioning systems. Such systems may be self-contained and/or “non-reference based” systems within the device or the platform, and thus need not depend upon external sources of information that can become interrupted or blocked.
One such “non-reference based” or relative positioning system is the inertial navigation system (INS). Inertial sensors are self-contained sensors within the device or platform that use gyroscopes to measure rate of rotation/angle, and accelerometers to measure specific force (from which acceleration is obtained). Using initial estimates of position, velocity and orientation angles of the device or platform as a starting point, the INS readings can subsequently be integrated over time and used to determine the current position, velocity and orientation angles of the device and its relative misalignment within the platform. Typically, measurements are integrated once for gyroscopes to yield orientation angles and twice for accelerometers to yield position of the device or platform incorporating the orientation angles. Thus, the measurements of gyroscopes will undergo a triple integration operation during the process of yielding position. Inertial sensors alone, however, are unsuitable for accurate positioning because the required integration operations of data results in positioning solutions that drift with time, thereby leading to an unbounded accumulation of errors.
Further problems in providing accurate position or navigation information about a mobile device can arise where the device is capable of moving freely (e.g. without any constraints) or can move with some constraints within the moving platform. Inaccuracies can arise in such cases because the coordinate frame of the inertial sensors (accelerometers and gyroscopes) of the device is not aligned with the coordinate frame of the moving platform. The device and the moving platform can be misaligned with respect to one another, and such misalignment can change over time. For example, where the device moves freely without constraint, the misalignment of the device and the platform can change without constraint. Where the device is capable of constrained movement, the misalignment of the device and the platform can also change, wherein the change is subject to constraints. Where the mobile device is mounted within the platform, there may still be a misalignment where such mounting results in a misalignment between the coordinate frame of the device and the coordinate frame of the platform (although such misalignment would not change over time). It should be noted that a skilled person would know and understand that the misalignment between a mobile device and a moving platform does not equate or relate to misalignment that might occur where a navigation module for positioning a moving platform is positioned incorrectly within the moving platform, thereby resulting in a misalignment between the module and the moving platform
Where available, another known complementary “non-reference based” system is a system for measuring speed/velocity information such as, for example, odometric information from a odometer within the platform. Odometric data can be extracted using sensors that measure the rotation of the wheel axes and/or steer axes of the platform (in case of wheeled platforms). Wheel rotation information can then be translated into linear displacement, thereby providing wheel and platform speeds, resulting in an inexpensive means of obtaining speed with relatively high sampling rates. Where initial position and orientation estimates are available, the odometric data are integrated thereto in the form of incremental motion information over time.
Given that the positioning techniques described above (whether INS/GNSS or INS/GNSS/Speed Information) may suffer loss of information or errors in data, common practice involves integrating the information/data obtained from the GNSS with that of the complementary system(s). For instance, to achieve a better positioning solution, INS and GPS data may be integrated because they have complementary characteristics. INS readings are accurate in the short-term, but their errors increase without bounds in the long-term due to inherent sensor errors. GNSS readings are not as accurate as INS in the short-term, but GNSS accuracy does not decrease with time, thereby providing long-term accuracy. Also, GNSS may suffer from outages due to signal blockage, multipath effects, interference or jamming, while INS is immune to these effects.
Although available, integrated INS/GNSS is not often used commercially for low cost applications because of the relatively high cost of navigational or tactical grades of inertial measurement units (IMUs) needed to obtain reliable independent positioning and navigation during GNSS outages. Low cost, small, lightweight and low power consumption Micro-Electro-Mechanical Systems (MEMS)-based inertial sensors may be used together with low cost GNSS receivers, but the performance of the navigation system will degrade very quickly in contrast to the higher grade IMUs in areas with little or no GNSS signal availability due to time-dependent accumulation of errors from the INS.
Speed information from the odometric readings, or from any other source, may be used to enhance the performance of the MEMS-based integrated INS/GNSS solution by providing velocity updates, however, current INS/Odometry/GNSS systems continue to be plagued with the unbounded growth of errors over time during GNSS outages.
One reason for the continued problems is that commercially available navigation systems using INS/GNSS integration or INS/Odometry/GNSS integration rely on the use of traditional Kalman Filter (KF)-based techniques for sensor fusion and state estimation. The KF is an estimation tool that provides a sequential recursive algorithm for the estimation of the state of a system when the system model is linear.
As is known, the KF estimates the system state at some time point and then obtains observation “updates” in the form of noisy measurements. As such, the equations for the KF fall into two groups:                Time update or “prediction” equations: used to project forward in time the current state and error covariance estimates to obtain an a priori estimate for the next step, or        Measurement update or “correction” equations: used to incorporate a new measurement into the a priori estimate to obtain an improved posteriori estimate.        
While the commonly used Linearalized KF (LKF) and Extended KF (EKF) can provide adequate solutions when higher grade IMUs are utilized by linearizing the originally nonlinear models, the KF generally suffers from a number of major drawbacks that become influential when using low cost MEMS-based inertial sensors, as outlined below.
The INS/GNSS integration problem at hand has nonlinear models. Thus, in order to utilize the linear KF estimation techniques in this type of problem, the nonlinear INS/GNSS model has to be linearized around a nominal trajectory. This linearization means that the original (nonlinear) problem be transformed into an approximated problem that may be solved optimally, rather than approximating the solution to the correct problem. The accuracy of the resulting solution can thus be reduced due to the impact of neglected nonlinear and higher order terms. These neglected higher order terms are more influential and cause error growth in the positioning solution, in degraded and GNSS-denied environments, particularly when low cost MEMS-based IMUs are used.
Further, the KF requires an accurate stochastic model of each of the inertial sensor errors, which can be difficult to obtain, particularly where low cost MEMS-based sensors are used because they suffer from complex stochastic error characteristics. The KF is restricted to use only linear low-order (low memory length) models for these sensors' stochastic errors such as, for example, random walk, Gauss-Markov models, first order Auto-Regressive models or second order Auto-Regressive models. The dependence of the KF on these inadequate models is also a drawback of the KF when using low cost MEMS-based inertial sensors.
As a result of these shortcomings, the KF can suffer from significant drift or divergence during long periods of GNSS signal outages, especially where low cost sensors are used. During these periods, the KF operates in prediction mode where errors in previous predictions, which are due to the stochastic drifts of the inertial sensor readings not well compensated by linear low memory length sensors' error models and inadequate linearized models, are propagated to the current estimate and summed with new errors to create an even larger error. This propagation of errors causes the solution to drift more with time, which in turn causes the linearization effect to worsen because of the drifting solution used as the nominal trajectory for linearization (in both LKF and EKF cases). Thus, the KF techniques suffer from divergence during outages due to approximations during the linearization process and system mis-modeling, which are influential when using MEMS-based sensors.
In addition, the traditional INS typically relies on a full inertial measurement unit (IMU) having three orthogonal accelerometers and three orthogonal gyroscopes. This full IMU setting has several sources of error, which, in the case of low-cost MEMS-based IMUs, will cause severe effects on the positioning performance. The residual uncompensated sensor errors, even after KF compensation, can cause position error composed of three additive quantities: (i) proportional to the cube of GNSS outage duration and the uncompensated horizontal gyroscope biases; (ii) proportional to the square of GNSS outage duration and the three accelerometers uncompensated biases, and (iii) proportional to the square of GNSS outage duration, the horizontal speed, and the vertical gyroscope uncompensated bias.
The foregoing drawbacks of the KF have resulted in increased investigation into alternative methods of INS/GNSS integration models, such as, for example, nonlinear artificial intelligence techniques. However, there is a need for enhancing the performance of low-end systems relying on low cost MEMS-based INS/GNSS sensors and for mitigating the effect of all sources of errors to provide a more adequate navigation solution for a device within a moving platform. This causes a need for a technique capable of using robust nonlinear models without linearization or approximation. Furthermore the needed technique should be able to cope with varying misalignment between the device and platform such as discussed earlier, especially in the case where the device moves freely without constraints within the moving platform.